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Bear in mind that both the below answers are correct, but updates on the underlying tables can force statistics updates on the indexes as well. This is probably less costly than updating the data in the index itself but it still is a cost to consider.
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JNK♦Jun 4 '13 at 20:27

If I capture the post execution plan of the UPDATE command, you will see something similar here:

As you see from the above screenshot, the indexes that are updated are the clustered index, and my nonclustered index IX_Col3. The index _idx_TableA does not get updated. Therefore, only the indexes that contain Col3 will be affected, and therefore updated by your particular example.